## Percentage Formulas in Maths

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Percentage Formulas in maths : The word “cent” is derived from the Latin word “per centum”, which means “up to a hundred”. Percentages are those fractions that have 100 as the denominator. In other words, it is the relation between the part and the whole where the value of the whole is always taken as 100.

### What is the percentage?

Percentage is a fraction or ratio in which the absolute value is always 100. For example, if Sam scored 30% on his math test, it means that he scored 30 out of 100. It is written as 30/100. 30:100 in terms of fractions and ratios.

Percentage Definition:

Percentage is defined as the part or amount given in every hundred. It is a fraction that has 100 as the denominator and is represented by the symbol “%”.

### Calculate percentage

To calculate the percentage means to find the part of the whole in terms of 100. There are two ways to find the percentage:

by using the unitary method.

Change the denominator of the fraction to 100.

It should be noted that the second method for calculating percentages is not used in situations where the denominator is not a factor of 100.

## How to get percentage

Percentage is another name for indicating hundredth. Thus, 1% is one hundredth, i.e. 1%=1/100=0.01.

Let us calculate the percentage using the above two methods.

When we have two or more values that add up to 100, that number is the percentage of those individual values to the total value. For example, Sally bought three different colored tiles for her house. The purchase details are given in the following table.

Colour | Number of Tiles | Rate per Hundred | Fraction | Written as | Read as |

Yellow | 39 | 39 | 39/100 | 39% | 39 percent |

Green | 26 | 26 | 26/100 | 26% | 26 percent |

Red | 35 | 35 | 35/100 | 35% | 35 percent |

Since the total number of items adds up to 100, the percentage can be easily calculated.

What if the total number of items doesn’t add up to 100? In such cases, we convert the fractions to equivalent fractions, in which the denominator is 100.

For example, Emma has a bracelet made of 20 beads of two different colors, red and blue. Look at the following table which shows the percentage of red and blue beads out of 20 beads.

Emma’s sisters, Nora and Jenny, also calculated the percentage, but in different ways.

Nora used the unitary method. Using the unitary method to calculate the percentage, we say that out of 20 beads, the number of red beads is 8. Therefore, out of 100, the number of red beads would be 8/20 × 100 = 40%.

Jenny multiplied the numerator and denominator by 5/5 to convert the fraction 8/20 to an equivalent fraction 40/100.

So, 8/20= (8×5)/(20×5)

= 40/100

= 40%

## Formula to calculate percentage

The percentage formula is used to find the part of a whole in terms of 100. you can represent a number as a fraction of 100 y Using this formula. If you look carefully, all the three methods of getting the percentage shown above can be easily calculated. By using the formula below:

Percentage = (Price / Total Value) × 100

## percentage difference between two numbers

Percentage difference is the change in the value of a quantity over a period of time in percentage terms. Sometimes we need to know the decrease

or increase in some quantity as a percentage, also known as percentage change. For example, increase in population, decrease in poverty, etc.

We have a formula to show the change in quantity as a percentage. Two cases can come up while calculating the percentage difference and they are:

calculate percentage increase

Calculate percentage reduction

How to calculate percentage increase?

Percentage increase refers to the interchangeable change in price when it is increased over a period of time. For example, increase in population, increase in the number of bacteria on the surface, etc. The percentage increase can be calculated using the following formula:

Percentage Increase = (Increased Value – Original Value) / Original Value × 100

### How to calculate percentage reduction?

Percentage reduction refers to the interchangeable change in price when it is reduced over a period of time. For example, reduction in rainfall levels, reduction in the number of covid patients etc. The percentage reduction can be calculated using the following formula:

Percentage reduction = (original value – reduced value) / original value × 100

## Percentage formula

To determine the percentage, we need to divide the price by the total price and then multiply the result by 100.

Percentage Formula = (Value/Total Value)×100

Example: 2/5 × 100 = 0.4 × 100 = 40 percent

How to calculate percentage of a number?

To calculate the percentage of a number, we have to use a different formula like:

P% of number = X

where X is the required percentage.

If we remove the % sign, we have to express the above formulas as;

p/100 * number = x

Example: Calculate 10% of 80.

Let 10% of 80 = X

10/100 * 80 = X

x = 8

### Percentage Difference Formula

If we are given two values and we want to find the percentage difference between the two values, it can be done by using the formula:

\(percentage~difference = \frac{\left|N_{1}-N_{2}\right|}{\left[\frac{\left(N_{1}+N_{2}\right)}{2 }\right]} \fold 100\)

For example, if 20 and 30 are two different values, the percentage difference between them would be:

% difference between 20 and 30 = \(percentage~difference = \frac{\left|20-30\right|}{\left [\frac{\left(20+30\right)}{2}\right] } \times 100\)

### Percentage increase and decrease

The percentage increase is equal to the subtraction of the original number from the new number, divided by the original number and multiplied by 100.

% increment = [(new number – original number)/original number] x 100

Where,

Increase in number = new number – original number

Similarly, the percentage decrease is equal to the subtraction of the new number from the original number, divided by the original number and multiplied by 100.

% decrease = [(original number – new number)/original number] x 100

where decrease in number = original number – new number

So basically if the answer is negative then there is a decrease of percentage.

#### points to remember:

- To find the percentage of the whole, find the value of 1% and then multiply by the percentage we want to find.
- Any increase or decrease in quantity can be expressed as a percentage.
- Fractions can be converted to percentages and vice versa.
- Percentages are reversible. For example, 25% of 40 is the same as 40% of 25.

## Solved Examples on Percentage Formulas in maths

Example 1:

Robert got a 5% increase in his salary. His current salary is $70,000. Calculate his revised pay after promotion.

Solution:

Robert’s current salary = $70,000

5% increase in salary means: 5% of 70,000 = 5/100 × 70,000

5 × 700 = $3500

Robert’s increment is $3500.

Thus, his new salary would be $70,000 + $3500 = $73,500.

Robert’s salary after promotion would be $73,500.

Example 2:

Neil bought a new cell phone for $90. The price of the phone drops by 3% every year from its original price. Find the cost of his mobile after 3 years.

Solution:

3% of 90 is: $2.7

The phone depreciates by $2.7 each year.

Thus, the value of the mobile after 3 years would be: 90 – (3×2.7) = $81.9

*-f*-er 3 years the value of mobile is $81.9 . Will happen